15.21.7 problem 29

Internal problem ID [3331]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 29
Date solved : Tuesday, March 04, 2025 at 04:36:14 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=y^{\prime } x +{\mathrm e}^{y^{\prime }} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 21

ode:=y(x) = x*diff(y(x),x)+exp(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= x \left (\ln \left (-x \right )-1\right ) \\ y \left (x \right ) &= c_{1} x +{\mathrm e}^{c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 26

ode=y[x]==D[y[x],x]*x+Exp[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x+e^{c_1} \\ y(x)\to x (\log (-x)-1) \\ \end{align*}

✓ Sympy. Time used: 24.237 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x) - exp(Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} - W\left (\frac {e^{\frac {y{\left (x \right )}}{x}}}{x}\right ) + \frac {y{\left (x \right )}}{x} = 0 \]